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The disagreement in the axial displacement indi-cates that the functional relations for some of the strain parts (thermal, creep, transient) or their materialparameters as taken in the present study have not been modelled with a sufficient accuracy to describe thematerials employed in the experiment. A further research will be needed to identify which of the strain partsneed the improvement.Next, we compared our numerical results for the resistance time with the predictions of the Europeanbuilding code Eurocode 2 (2002). For the clamped column, our method predicted the resistance time214 min for the partially insulated column, and 212 min for the uninsulated one. This is very close tothe experimentally found value 208 min. By contrast, the Eurocode predicted much shorter resistance time,181 min, when the set of simply supported columns was studied in our second numerical example. Wefound that Eurocode 2 predicted about 10% longer resistance time than calculated with our method. Thisis a surprise, because standards are assumed to give conservative, the safe side results. Only further system-atic and well documented experimental analyses could resolve the question if this is indeed so.ReferencesAnderberg, Y., Thelandersson, S., 1976. Stress and Deformation Characteristics of Concrete at High Temperatures, 2. ExperimentalInvestigation and Material Behaviour Model. Lund Institute of Technology, Sweden.ASTM E-119-76, 1976. Standard Methods of Fire Tests of Building Construction and Materials, Annual book of ASTM standards,Parts 18, American Society for Testing and Materials.Bratina, S., Saje, M., Planinc, I., 2003a. On materially and geometrically non-linear analysis of reinforced concrete planar frames,Internal report 1/2003, University of Ljubljana, Faculty of Civil and Geodetic Engineering, Chair of Mechanics, 49p.Bratina, S., Planinc, I., Saje, M., Turk, G., 2003b. Non-linear fire-resistance analysis of reinforced concrete beams. StructuralEngineering and Mechanics 16 (6), 695–712.Bratina, S., Saje, M., Planinc, I., 2004. On materially and geometrically non-linear analysis of reinforced concrete planar frames.International Journal of Solids and Structures 41 (6), 7181–7207.Cai, J., Burgess, I., Plank, R., 2003. A generalised steel/reinforced concrete beam-column element model for fire conditions.Engineering Structures 25 (6), 817–833.Cioni, P., Croce, P., Salvatore, W., 2001. Assessing fire damage to r.c. elements. Fire Safety Journal 36, 181–199.Cruz, C.R., 1968. Apparatus for measuring creep of concrete at high temperatures. Journal of the PCA Research and DevelopmentLaboratories 10 (3), 36–42.Dotreppe, J.-C., Franssen, J.-M., Vanderzeypen, Y., 1999. Calculation method for design of reinforced concrete columns under fireconditions. ACI Structural Journal 96 (1), 9–18.Ellingwood, B., Lin, T.D., 1991. Flexure and shear behaviour of concrete beams during fires. ASCE Journal of Structural Engineering117 (2), 440–458.Eurocode 1, 1995. Basis of Design and Actions on Structures, Part 2-2: Actions on structures–Actions on structures exposed to fire,ENV 1991-2-2. Eurocode 2, 1991. Design of Concrete Structures, Part 1: General rules and rules for buildings, ENV 1992-1-1.Eurocode 2, 2002. Design of Concrete Structures, Part 1-2: General rules–Structural Fire Design, prEN 1992-1-2.Franssen, J.-M., Dotreppe, J.-C., 2003. Fire tests and calculation methods for circular concrete columns. Fire Technology 39, 89–97.Harmathy, T.Z., 1993. Fire Safety Design and Concrete. Longman, London.Huang, Z., Burgess, I.W., Plank, J.R., 1999. Nonlinear analysis of reinforced concrete slabs subjected to fire. ACI Structural Journal96 (1), 127–135.Huang, Z., Platten, A., Roberts, J., 1996. Non-linear finite element model to predict temperature histories within reinforced concrete infire. Building and Environment 31 (2), 109–153.Lie, T.T., Celikkol, B., 1991.
Method to calculate the fire resistance of circular reinforced concrete columns. ACI Materials Journal 88(1), 84–91.Lie, T.T., Irwin, R.J., 1993. Method to calculate the fire resistance of reinforced concrete columns with rectangular cross section. ACIStructural Journal 90 (1), 52–60.Lin, T.D., Ellingwood, B., Piet, O., 1988. Flexural and shear behaviour of reinforced concrete beams during fire tests, PCA Researchand Development Bulletin, Report No. NBS-GCR-87-536, Center for Fire Resarch, National Bureau of Standards, Washington.Lin, T.D., Zwiers, R.I., Burg, R.G., Lie, T.T., McGrath, R.J., 1992. Fire resistance of reinforced concrete columns, PCA Research andDevelopment Bulletin, RD101B.Kodur, W.K.R., Wang, T.C., Cheng, F.P., 2004. Predicting the fire resistance behaviour of high strength concrete columns. Cementand Concrete Composites 26, 141–153.Najjar, S.R., Burgess, I.W., 1996. A nonlinear analysis of three-dimensional steel frames in fire conditions. Engineering Structures 18(1), 77–89.Planinc, I., Saje, M., C ˇ as, B., 2001. On the local stability condition in the planar beam finite element. Structural Engineering andMechanics 12 (5), 507–526.Reissner, E., 1972. On one-dimensional finite-strain beam theory: the plane problem. Journal of Applied Mathematics and Physics(ZAMP) 23, 795–804.Saje, M., Turk, G., (1987). HEATC, Computer programme for non-linear transient heat conduction problems, University ofLjubljana, Faculty of Civil and Geodetic Engineering, Ljubljana.Sidibe ´, K., Duprat, F., Pinglot, M., Bourret, B., 2000. Fire safety of reinforced concrete columns. ACI Structural Journal 97 (4), 642–647.The MathWorks, Inc., MATLAB 1999. Natick, Available from: <http://www.mathworks.com>.Williams-Leir, G., 1983. Creep of structural steel in fire: analytical expressions. Fire and Materials 7 (2), 73–78.Vratanar, B., Saje, M., 1998. A consistent equilibrium in a cross-section of an elastic–plastic beam. International Journal of Solids andStructures 36, 311–337.Zha, X.X., 2003. Three-dimensional non-linear analysis of reinforced concrete members in fire. Building and Environment 38, 297–307.Zhao, J.-C., 2000. Application of the direct iteration method for non-linear analysis of steel frames in fire. Fire Safety Journal 35, 241–255.
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